Answer:
<h2>20</h2>
<em>Solution</em><em>,</em>
<em><</em><em>N=</em><em>1</em><em>8</em><em>0</em><em>-</em><em>5</em><em>3</em><em>-</em><em>4</em><em>4</em>
<em> </em><em> </em><em> </em><em> </em><em>=</em><em>8</em><em>3</em>
<h3>
<em>Apply </em><em>sines </em><em>rule,</em></h3>
<em>
</em>
<em>hope </em><em>this </em><em>helps.</em><em>.</em>
<em>Good </em><em>luck</em><em> on</em><em> your</em><em> assignment</em><em>.</em><em>.</em>
Hi hi hi hi hi hi hi hi hi hi hi hi hi hi hi hi hi hi hi hi hi hi hi
Answer:
The simplified expression is : -9c +1
Step-by-step explanation:
The like terms are -8c and -c
The constant term is 1
The simplified expression is :
-8c + -c + 1 = -9c +1
![f(x)=x^3+5x^2+4x-6](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E3%2B5x%5E2%2B4x-6)
![f(-3)=(-3)^3+5(-3)^2+4(-3)-6=0\implies x+3\text{ is a factor of }f(x)](https://tex.z-dn.net/?f=f%28-3%29%3D%28-3%29%5E3%2B5%28-3%29%5E2%2B4%28-3%29-6%3D0%5Cimplies%20x%2B3%5Ctext%7B%20is%20a%20factor%20of%20%7Df%28x%29)
Synthetic division yields
-3 | 1 5 4 -6
. | -3 -6 6
- - - - - - - - - - - - -
. | 1 2 -2 0
which translates to
![\dfrac{x^3+5x^2+4x-6}{x+3}=x^2+2x-2](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%5E3%2B5x%5E2%2B4x-6%7D%7Bx%2B3%7D%3Dx%5E2%2B2x-2)
with remainder 0. Now by the quadratic formula,
![x^2+2x-2=0\implies x=\dfrac{-2\pm\sqrt{2^2-4(1)(-2)}}2=-1\pm\sqrt3](https://tex.z-dn.net/?f=x%5E2%2B2x-2%3D0%5Cimplies%20x%3D%5Cdfrac%7B-2%5Cpm%5Csqrt%7B2%5E2-4%281%29%28-2%29%7D%7D2%3D-1%5Cpm%5Csqrt3)
and so
Had -9-x^2
———
x^2
adh (-9-x^2)
——————-
x^2
-9adh-adhx^2
———————
x^2
9adh+adhx^2
- ———————
x^2
Hope this helps